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Topic: An interesting property of ellipses
Replies: 1   Last Post: Jun 23, 1994 12:21 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: An interesting property of ellipses
Posted: Jun 23, 1994 12:21 PM
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This is, or really I should say "was", a well-known property.
The locus of points from which an ellipse subtends a right angle
is usually called the "director circle", because the corresponding
locus for a parabola is its directrix.

Here's something you may like. Take a loop of string around your`
ellipse, into which you're going to put your pencil-point and
use it to draw a circumscribing curve, in a way that specializes
to the usual way of drawing an ellipse when the starting ellipse
degenerates to a line segment.

Then the curve you draw will be a confocal ellipse to the
original, and both the part of the string that touches the
inner ellipse, and the part that doesn't, remain of
constant length.

John Conway

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